Asymptotic normality in Monte Carlo integration
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- by Masashi Okamoto PDF
- Math. Comp. 30 (1976), 831-837 Request permission
Abstract:
To estimate a multiple integral of a function over the unit cube, Haber proposed two Monte Carlo estimators $J’_1$ and $J’_2$ based on 2N and 4N observations, respectively, of the function. He also considered estimators $D_1^2$ and $D_2^2$ of the variances of $J’_1$ and $J’_2$, respectively. This paper shows that all these estimators are asymptotically normally distributed as N tends to infinity.References
- Seymour Haber, A modified Monte-Carlo quadrature, Math. Comp. 20 (1966), 361–368. MR 210285, DOI 10.1090/S0025-5718-1966-0210285-0
- Seymour Haber, A modified Monte-Carlo quadrature. II, Math. Comp. 21 (1967), 388–397. MR 234606, DOI 10.1090/S0025-5718-1967-0234606-9
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Math. Comp. 30 (1976), 831-837
- MSC: Primary 65C05
- DOI: https://doi.org/10.1090/S0025-5718-1976-0421029-8
- MathSciNet review: 0421029